A Level Set Method for the Inverse Problem of Wave Equation in the Fluid-Saturated Porous Media (Communications in Computational Physics, 2009)
In this paper, a level set method is applied to the inverse problem of 2-Dwave equation in the fluid-saturated media. We only consider the situation that theparameter to be recovered takes two different values, which leads to a shape reconstructionproblem. A level set function is used to present the discontinuous parameter,and a regularization functional is applied to the level set function for the ill-posedproblem. Then the resulting inverse problem with respect to the level set function issolved by using the damped Gauss-Newton method. Numerical experiments showthat the method can recover parameter with complicated geometry and the noise inthe observation data.